What is the visual representation of the function y = x^2 compared to y = √x?

The correct choice highlights the fundamental difference in the nature of the two functions. The function y = x^2 is indeed a parabola that opens upwards, demonstrating a quadratic relationship in which the y-values increase rapidly as x moves away from zero in both the positive and negative directions. This shape results from squaring the input value, creating a curve that reflects the properties of quadratic functions, particularly the symmetry and the vertex at the origin (0,0).

On the other hand, the function y = √x represents a different relationship altogether. It is defined only for non-negative values of x (x ≥ 0) and produces a curve that starts at the origin and gradually increases, approaching but never reaching the line y = x. This function represents a radical relationship, which emphasizes the square root's slow growth compared to the quadratic function.

By understanding these distinct characteristics, one can easily see that y = x^2 is a parabolic shape, while y = √x does not exhibit this behavior, thus verifying the correctness of the statement that y = x^2 is a parabola, whereas y = √x is not.